An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

Abstract

This work introduces an indirect Boundary Element Method (BEM) within a NURBS-based isogeometric framework for solving three-dimensional acoustic problems in the frequency domain. Developments of isogeometric boundary elements so far have focused on the direct BEM. Yet, a multitude of common problems in acoustics involves open-boundary surfaces, which require a more involved, indirect, boundary element formulation. The current work presents an indirect variational BEM which makes use of NURBS shape functions. Additionally, a novel technique for coupling (strongly) non-conforming patches is introduced to allow the analysis of more complex geometries. The proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial-based indirect BEM. Also two open-boundary problems are studied, including analyses over wider frequency ranges, and one industrial-type, complex geometry containing multiple non-conforming patches. The proposed method is found to be not only significantly more efficient than its polynomial-based counterpart, but also very robust against strong non-conformities in the NURBS descriptions.